How do I make a curve in the shape of a simple wave form (sine)?
Animation Node can be used here, a simple sine wave spline can be generated as follows:



Animating an object along the wave can be done by evaluating it at some point as follows:



Where the divide controls the speed of the motion.

To align the rotation of the object, you can compute the angle that the tangent to the curve makes with the x axis, the tangent is equal to the derivative which is dy/dt(sin(t)) = cos(t) so the angle is equal to arctan(cos(t)), and the node tree becomes as follows: